1hill1.mac and hill2.mac are from the book "Computer Algebra in Applied 2Mathematics: An introduction to MACSYMA", by Richard H Rand, Pitman 3(1984). 4 5Mathieu's equation is x''+(delta+e*cos(t))*x=0 6 7For given values of the parameters delta and e, either all the 8solutions are bounded (the equation is stable) or there exist 9unbounded solutions (the equation is unstable). The regions of 10stability are separated from thos of instability by "transition 11curves". 12 13This program computes the transition curves of Mathieu's equation 14using Fourier series to obtain Hill's determinants. 15 16The run below, using maxima-5.9.0cvs, reproduces the result on pages 17108-109 of the book. The results are identical to those from 18mathieu0.mac and mathieu.mac. 19 20 21(C1) load("./hill1.mac"); 22(D1) ./hill1.mac 23(C2) load("./hill2.mac"); 24(D2) ./hill2.mac 25(C3) hill(); 26ENTER TRANSITION CURVE NUMBER N 270; 28ENTER DEGREE OF TRUNCATION 296; 30 6 4 2 31 29 e 7 e e 32delta= - ----- + ---- - -- 33 144 32 2 34 35(D3) FALSE 36(C4) hill(); 37ENTER TRANSITION CURVE NUMBER N 381; 39ENTER DEGREE OF TRUNCATION 406; 41 6 5 4 3 2 42 49 e 11 e e e e e 1 43delta= ----- - ----- - --- + -- - -- - - + - 44 36864 4608 384 32 8 2 4 45 46 6 5 4 3 2 47 49 e 11 e e e e e 1 48delta= ----- + ----- - --- - -- - -- + - + - 49 36864 4608 384 32 8 2 4 50 51(D4) 52(C5) hill(); 53ENTER TRANSITION CURVE NUMBER N 542; 55ENTER DEGREE OF TRUNCATION 566; 57 6 4 2 58 1002401 e 763 e 5 e 59delta= ---------- - ------ + ---- + 1 60 4976640 3456 12 61 62 6 4 2 63 289 e 5 e e 64delta= - ------- + ---- - -- + 1 65 4976640 3456 12 66 67 68 69Local Variables: *** 70mode: Text *** 71End: ***